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Good reduction of 1-motives

URN to cite this document: urn:nbn:de:bvb:703-epub-1721-1

Title data

Matev, Tzanko:
Good reduction of 1-motives.
Bayreuth , 2014 . - IX, 115 P.
( Doctoral thesis, 2013 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

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Project information

Project title:
Project's official titleProject's id
DFG-Schwerpunktprogramm 1489: Algorithmic and experimantal algebraic geometryNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract

In this dissertation we study 1-motives over number fields and their application to questions dealing with reductions of points in semiabelian varieties. We prove a version of the Néron-Ogg-Shafarevich criterion for 1-motives and show how the image of the Frobenius in the ℓ-adic Galois representation associated to a 1-motive determines the ℓ-part of its reduction modulo the corresponding prime. We use this theory to investigate a family of properties for points in tori which we call algebraic dependences. In particular, we study the rank of the reduction of a group generated by two rational points in G2m, modulo different primes. Finally, we show how our algebraic dependences exhibit an analogy between problems in p-adic transcendence theory and problems concerning reduction of points.

Abstract in another language

In dieser Doktorarbeit werden 1-Motive über Zahlkörpern und ihre Anwendung auf Fragen über die Reduktion von Punkten in semiabelschen Varietäten untersucht. Es wird eine Version des Néron-Ogg-Shafarevich-Kriteriums für 1-Motive bewiesen und es wird beschrieben, wie das Bild des Frobenius-Automorphismus in der dem 1-Motiv zugeordneten ℓ-adischen Galoisdarstellung die Reduktion modulo dem entsprechenden Primideal bestimmt. Wir wenden die von uns entwickelte Theorie an, um eine Familie von Eigenschaften für Punkte auf Tori zu untersuchen, die wir „algebraische Abhängigkeiten“ nennen. Ins besondere wird der Rang der Reduktion modulo verschiedenen Primidealen einer von zwei rationalen Punkten in G2m erzeugten Gruppe untersucht. Schließlich wird gezeigt, dass unsere algebraischen Abhängigkeiten eine Analogie zwischen gewissen Probleme der p-adischen Transzendenztheorie und Problemen bezüglich Reduktion von Punkten vermitteln.

Further data

Item Type: Doctoral thesis (No information)
Keywords: number theory; 1-motives; reduction; Tate module
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Graduate Schools
Graduate Schools > University of Bayreuth Graduate School
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-1721-1
Date Deposited: 17 Sep 2014 13:55
Last Modified: 15 May 2015 09:10
URI: https://epub.uni-bayreuth.de/id/eprint/1721

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